Definition 3.3.14 (One-to-one functions). A function \(f\) is one-to-one (or injective) if different elements map to different elements: $$ x\neq x'\implies f(x)\neq f(x') $$
Equivalently, a function is one-to-one if $$ f(x)=f(x')\implies x=x' $$
Definition 3.3.14 (One-to-one functions). A function \(f\) is one-to-one (or injective) if different elements map to different elements: $$ x\neq x'\implies f(x)\neq f(x') $$
Equivalently, a function is one-to-one if $$ f(x)=f(x')\implies x=x' $$
\(\equiv\) { Definition 3.3.14 }
\(\equiv\) { Definition 3.3.14 }